{"id":{"repo_id":"ku","oai_identifier":"oai:kuscholarworks.ku.edu:1808/39470"},"canonical_url":"https://search.dev.ndltd.org/etd/ku/oai:kuscholarworks.ku.edu:1808/39470","repository":{"repo_id":"ku","name":"University of Kansas","base_url":"https://kuscholarworks.ku.edu/server/oai/request"},"display":{"title":"On special Kähler metrics and hypersurfaces","abstract":"Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. In this dissertation, we study these special Kähler metrics and hypersurfaces in Kähler Ricci-flat spaces. Particularly, we determine the second fundamental form of the sphere inthe Euclidean sense in Eguchi-Hanson spaces, motivated by constructing constant mean curvature hypersurfaces. We quantify how far these spheres are from being umbilic.","abstract_html":"Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. In this dissertation, we study these special Kähler metrics and hypersurfaces in Kähler Ricci-flat spaces. Particularly, we determine the second fundamental form of the sphere inthe Euclidean sense in Eguchi-Hanson spaces, motivated by constructing constant mean curvature hypersurfaces. We quantify how far these spheres are from being umbilic.","abstract_has_math":false,"creators":["Gong, Sien"],"institution":"University of Kansas","degree_name":"Ph.D.","degree_level":null,"degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Wang, Yuanqi"],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-05-31","date_published":"2026-05-31","updated_at":"2026-07-24T02:45:54Z","subjects":["Eguchi-Hanson","Second Fundamental Form"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/32701256"],"render_values":[{"text":"https://www.proquest.com/LegacyDocView/DISSNUM/32701256","href":"https://www.proquest.com/LegacyDocView/DISSNUM/32701256","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1808/39470","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Wang, Yuanqi"]},{"key":"dc:creator","label":"Author","values":["Gong, Sien"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-07-15T20:23:18Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-07-15T20:23:18Z"]},{"key":"dc:date.issued","label":"Date","values":["2026-05-31"]},{"key":"dc:publisher","label":"Institution","values":["University of Kansas"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Eguchi-Hanson","Second Fundamental Form"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/32701256"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1808/39470"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. In this dissertation, we study these special Kähler metrics and hypersurfaces in Kähler Ricci-flat spaces. Particularly, we determine the second fundamental form of the sphere inthe Euclidean sense in Eguchi-Hanson spaces, motivated by constructing constant mean curvature hypersurfaces. We quantify how far these spheres are from being umbilic."]},{"key":"dc:title","label":"Title","values":["On special Kähler metrics and hypersurfaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Wang, Yuanqi"],"dc:creator":["Gong, Sien"],"dc:date.accessioned":["2026-07-15T20:23:18Z"],"dc:date.available":["2026-07-15T20:23:18Z"],"dc:date.issued":["2026-05-31"],"dc:description.abstract":["Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. In this dissertation, we study these special Kähler metrics and hypersurfaces in Kähler Ricci-flat spaces. Particularly, we determine the second fundamental form of the sphere inthe Euclidean sense in Eguchi-Hanson spaces, motivated by constructing constant mean curvature hypersurfaces. We quantify how far these spheres are from being umbilic."],"dc:identifier.other":["https://www.proquest.com/LegacyDocView/DISSNUM/32701256"],"dc:identifier.uri":["https://hdl.handle.net/1808/39470"],"dc:language.iso":["en"],"dc:publisher":["University of Kansas"],"dc:subject":["Eguchi-Hanson","Second Fundamental Form"],"dc:title":["On special Kähler metrics and hypersurfaces"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:45:54Z"}